The Anfield club agreed a £67million fee with Roma earlier on Wednesday.
And according to Sky Italy , Alisson has spoken to Liverpool boss Jurgen Klopp and verbally agreed to join the Champions League finalists.
The Brazil No.1 will now travel to Liverpool to undergo his medical before putting pen to paper.
His move to Merseyside represents a blow to Chelsea who had hoped to gazump their Premier League rivals with a £70million offer.
This story has been reproduced from the media. It does not necessarily represent the position of Liverpool Football Club.